Six ‘$+$’ and four ‘$-$’ signs are to placed in a straight line so that no two ‘$-$’ signs come together, then the total number of ways are

If $^n{P_3}{ + ^n}{C_{n - 2}} = 14n$, then $n = $

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

Let $A = \left\{ {{a_1},\,{a_2},\,{a_3}.....} \right\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of it is formed independently. The number of ways in which subsets can be formed such that $(P-Q)$ contains exactly $2$ elements, is

An urn contains $5$ red marbles, $4$ black marbles and $3$ white marbles. Then the number of ways in which $4$ marbles can be drawn so that at the most three of them are red is

How many words can be made from the letters of the word $BHARAT$ in which $ B $ and $H$ never come together